|
MATHEMATICAL ANALYSIS III
|
| Course Name |
Code |
Regular Semester |
ECTS Credits |
Credits |
Lecture |
4
|
| Application |
2
|
|
Mathematical Analysis III
|
0252011
|
3
|
7.5
|
5
|
Laboratory (Hour/Week) |
-
|
|
| Course Language |
Turkish
|
| Compulsory or Elective |
Compulsory
|
| Equipment |
Board, Overhead Projector, Projector, Notebook, CD
|
| Instructor |
Department of Mathematics
|
| Course Contents |
Functions of several variables/ Limits/ Continuity and uniform continuity/ Partial derivative/ Total differential/ Fundamental theorem of differential/ Close and inverse functions/ Jakobien/ Taylor, Maclaurin formulas and series for functions of several variables/ Lagrange multipliers/ Vector-valued functions/ Gradient, divergence, rotasional, laplasien/ Directional derivatives/ Line coordinates
|
| Course Objectives |
-
To give fundamentals of mathematics knowledge
-
To be able to analyse the problem which are met in the fields of mathematics and to gain the ability of problem solving
-
To gain analytical thinking, discussion and evaluation
|
Course Outcomes
(The knowledge and the skills that the student will gain at the end of the course) |
-
To have the fundamentals of mathematical knowledge and culture
-
To have analytical thinking and evaluation
-
The skill of evaluation and studying the problems which occur in other disciplines
|
| Textbook |
Lecture notes
|
| Additional References |
-
“Advanced Calculus” Wilfred Kaplan Wesley-Publishing Company, 1984
-
Advanced Calculus” David V. Widder , Prentice-Hall,1968
-
“Calculus” Thomas- Finney Addison-Wesley , 1998
|
|
| Prerequisite Courses |
-
|
| Prerequisite Subjects |
0251011 Anaysis 1 subjects
|
| Homework/Project |
-
|
| Laboratory |
-
|
| Computer Applications |
-
|
| Additional Practices |
-
|
|
| Course Evaluation Criteria |
|
Number |
Effective Proportion % |
| Midterm Exams |
2
|
60
|
| Quiz |
-
|
-
|
| Homework |
-
|
-
|
| Term Projects |
-
|
-
|
| Term Papers |
-
|
-
|
| Laboratory |
-
|
-
|
| Other |
-
|
-
|
| Final Exam |
1
|
40
|
|
| Division of Course Credit (%) |
Basic Sciences |
-
% |
| Basic Engineering and Departmental Core Courses |
-
% |
| Departmental Core Courses |
100
% |
| Social Sciences |
-
% |
|
|
| WEEKLY COURSE PLAN |
| Week |
Subject |
| 1 |
Functions of several variables. Limits. Continuity and uniform continuity. Partial derivative.
|
| 2 |
Functions of several variables. Limits. Continuity and uniform continuity. Partial derivative.
|
| 3 |
Compound functions and its derivative
|
| 4 |
Total differential. Fundamental theorem of differential
|
| 5 |
Close and inverse functions
|
| 6 |
Jakobien
|
| 7 |
Taylor, Maclaurin formulas and series for functions of several variables
|
| 8 |
1st Midterm exam
|
| 9 |
Maximum and Minimum in Functions of several variables
|
| 10 |
Lagrange multipliers
|
| 11 |
Vector-valued functions
|
| 12 |
Gradient, divergence, rotasional, laplasien
|
| 13 |
2nd Midterm exam
|
| 14 |
Directional derivatives
|
| 15 |
Line coordinates
|
|
|
| Prepared by |
Department of Mathematics
|
Date |
01.01.2007
|
|